How do you solve $sin3 theta = -1$ if $(0 < theta < 2pi)$ ?

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Answer 1 · 2016-04-18T16:01:06

$S={pi/2, (7pi)/6, (11pi)/6}$

$3theta=sin^-1 (-1)$

$3theta=(3pi)/2 +2pin$

$theta=(3pi)/2 xx 1/3 +2pin xx 1/3$

$theta=pi/2+(2pi)/3 n$

Now put in n values. Remember n values are integers.
$n=0, x=pi/2$

$n=1, x=(7pi)/6$

$n=2, x=(11pi)/6$

$n=3,x=(5pi)/2 > 360$ so we stop

$S={pi/2, (7pi)/6, (11pi)/6}$

How do you solve sin3 theta = -1sin3 theta = -1 if (0 < theta < 2pi)(0 < theta < 2pi)?